"It shouldn't come as a shock, but Simon and Lauren really seem to be planning to name their son Simon!" the eyewitness exclusively told RadarOnline.com.
"There were baby clothes and little games all personalized with the name 'Simon' for the baby."
According to the source, there was also a lot of chatter at the party about their son-to-be, Simon.
"From what everyone — including Lauren — was saying, they are 100 percent naming their son Simon," the insider revealed.
"Initials for baby Simon were everywhere."
Cowell, 54, put together the English tea-themed party for Silverman, 36, at his Beverly Hills mansion but didn't attend the soiree.
The baby boy is due in February and it's the first child for Cowell and Silverman.
What do you think about a Simon Jr.? Sound off in the comments below…